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Sudoku Solution Path

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Copyright © Kevin Stone

R4C5 can only be <7>
R5C4 can only be <6>
R5C6 can only be <3>
R7C4 can only be <9>
R5C1 can only be <9>
R6C5 can only be <1>
R6C7 can only be <6>
R5C5 can only be <8>
R6C3 can only be <3>
R4C7 can only be <9>
R3C4 can only be <5>
R4C3 can only be <6>
R5C3 can only be <4>
R2C2 is the only square in row 2 that can be <5>
R1C7 is the only square in row 1 that can be <5>
R3C1 is the only square in row 3 that can be <7>
R7C8 is the only square in row 7 that can be <7>
R9C3 is the only square in row 9 that can be <5>
R9C8 is the only square in column 8 that can be <6>
Intersection of column 3 with block 1. The value <9> only appears in one or more of squares R1C3, R2C3 and R3C3 of column 3. These squares are the ones that intersect with block 1. Thus, the other (non-intersecting) squares of block 1 cannot contain this value.
   R1C2 - removing <9> from <1369> leaving <136>
   R3C2 - removing <9> from <139> leaving <13>
Intersection of column 8 with block 3. The value <1> only appears in one or more of squares R1C8, R2C8 and R3C8 of column 8. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
   R1C9 - removing <1> from <1249> leaving <249>
   R3C7 - removing <1> from <1238> leaving <238>
   R3C9 - removing <1> from <12489> leaving <2489>
Squares R2C5 and R2C8 in row 2 and R8C5 and R8C8 in row 8 form a Simple X-Wing pattern on possibility <2>. All other instances of this possibility in columns 5 and 8 can be removed.
   R1C5 - removing <2> from <249> leaving <49>
   R1C8 - removing <2> from <1239> leaving <139>
   R3C8 - removing <2> from <1239> leaving <139>
   R9C5 - removing <2> from <234> leaving <34>
Squares R9C5 (XY), R9C1 (XZ) and R7C6 (YZ) form an XY-Wing pattern on <2>. All squares that are buddies of both the XZ and YZ squares cannot be <2>.
   R7C1 - removing <2> from <236> leaving <36>
   R7C3 - removing <2> from <12> leaving <1>
R9C1 is the only square in block 7 that can be <2>
Squares R1C3<29>, R1C5<49> and R1C9<249> in row 1 form a comprehensive locked triplet. These 3 squares can only contain the 3 possibilities <249>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R1C8 - removing <9> from <139> leaving <13>
Squares R1C1, R7C1, R1C2 and R7C2 form a Type-4 Unique Rectangle on <36>.
   R1C2 - removing <3> from <136> leaving <16>
   R7C2 - removing <3> from <346> leaving <46>
Squares R1C5 (XY), R3C6 (XZ) and R1C3 (YZ) form an XY-Wing pattern on <2>. All squares that are buddies of both the XZ and YZ squares cannot be <2>.
   R3C3 - removing <2> from <29> leaving <9>
R1C3 can only be <2>
Squares R3C2 and R3C8 in row 3 form a simple locked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R3C7 - removing <3> from <238> leaving <28>
Squares R1C8 and R3C8 in column 8 form a simple locked pair. These 2 squares both contain the 2 possibilities <13>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R8C8 - removing <3> from <239> leaving <29>
Squares R9C9 (XY), R5C9 (XZ) and R8C8 (YZ) form an XY-Wing pattern on <2>. All squares that are buddies of both the XZ and YZ squares cannot be <2>.
   R7C9 - removing <2> from <28> leaving <8>
R3C7 is the only square in row 3 that can be <8>
Squares R7C6 (XY), R7C7 (XZ) and R9C5 (YZ) form an XY-Wing pattern on <3>. All squares that are buddies of both the XZ and YZ squares cannot be <3>.
   R9C7 - removing <3> from <13> leaving <1>
R9C9 can only be <9>
R5C7 can only be <2>
R1C9 can only be <4>
R8C8 can only be <2>
R1C5 can only be <9>
R3C9 can only be <2>
R3C6 can only be <4>
R5C9 can only be <1>
R2C8 can only be <9>
R7C7 can only be <3>
R7C1 can only be <6>
R8C5 can only be <3>
R2C5 can only be <2>
R7C6 can only be <2>
R7C2 can only be <4>
R1C1 can only be <3>
R9C2 can only be <3>
R8C2 can only be <9>
R9C5 can only be <4>
R3C2 can only be <1>
R1C8 can only be <1>
R1C2 can only be <6>
R3C8 can only be <3>

[Puzzle Code = Sudoku-20191206-SuperHard-044209]

 

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